Nondestructive methods for measuring the dielectric properties of materials are needed in biomedical and industrial applications. Because the interaction of an electromagnetic field with a material is highly dependent upon the electrical properties of that material, many electrical properties of a material may be determined by measuring how an electromagnetic wave interacts with that material. However, the precision with which one can determine how an electromagnetic wave interacts with a given material depends upon how accurately the complex permittivity of the material is known. A method for determining the complex permittivity is thus needed.
An accurate determination of the complex permittivity of a sample can be beneficial in carrying out certain biomedical procedures, such as electromagnetic thawing of cryo-preserved organs and tissues, electromagnetically-induced hyperthermia in cancer treatment, detection of pathological conditions in tissues and diagnostic monitoring applications such as lung water content. Since these processes are often carried out at microwave frequencies, the complex permittivity, which is frequency dependent, is of particular interest at microwave frequencies.
Industrial uses of complex permittivity measurements include monitoring the electrical characteristics of a material produced by or used in a manufacturing process. For example, water content of a material may be monitored by measuring the electrical characteristics of the material. Industrial processes may require that the complex permittivity be measured continuously or at frequent intervals as a material passes the measurement point on a production line. Such uses require that the permittivity be determined in "real time" (nearly instantaneously), so that appropriate action may be taken if a flaw is detected.
Conventional methods of determining complex permittivity at microwave frequencies are unsuitable for use in biomedical or industrial applications. For example, one method requires cutting, polishing and then placing the sample in a suitable waveguide or cavity. Another method, utilizing free-space techniques, is based on the reflection and transmission of electromagnetic waves radiated by a narrow beam antenna. This method requires that the sample have a relatively large plane surface. Samples used in biomedical or industrial applications often do not provide such a large plane surface.
Coaxial line excited monopole probes have been suggested for use in the electrical characterization of materials. However, an electric monopole probe is frequency sensitive and useful only when it is inserted into the material medium. Further, an electric monopole probe requires a relatively large sample volume which is not practical in many cases.
Prior art methods have attempted using an open-ended coaxial line for electrical characterization of a sample because using such a method should not require destruction of the sample and would be useful over a broad frequency band. Utilizing a coaxial line or probe to electrically characterize a material entails measuring the reflection coefficient or input impedance of a sample material and, from the measured data, determining the dielectric properties of the material. Prior art methods have not been successful in providing an effective way to relate the measured data to the dielectric properties of the material.
In one approach, nomograms are generated at three frequencies to determine the complex permittivity of a material from the measured reflection coefficient for an SR7 type coaxial line at the three frequencies. See Mosig et. al., "Reflection of an Open-ended Coaxial Line and Application to Nondestructive Measurement of Materials," IEEE Transactions Instrum. Meas., Vol. IM. 30, No. 1, pp. 46-51, March, 1981. However, since many more nomograms are necessary to cover the entire frequency range, and each set of nomograms is useful with only one probe, this method is not very practical. Moreover, generating the nomograms requires a large number of time consuming numerical computations.
Another prior art approach uses equivalent circuit parameters determined by the numerical computations of the nomogram method and empirical relations to provide an improved model having an acceptable accuracy up to only about 2 GHz. See Stuckly et. al., Measurement of Radiofrequency Permittivity of Biological Tissues with an Open-ended Coaxial Line, IEEE Transactions Microwave Theory Tech., Vol. MTT-30, pp. 87-92, January, 1982.
More recently, the permittivity has been determined from measured data utilizing a bilinear transformation to account for imperfections in the measuring system in conjunction with an equivalent circuit model for a coaxial opening. See, Marzland and Evans,
"Dielectric Measurements With an Open-ended Coaxial Probe," Proc. Inst. Elec. Eng., Vol. 134, pp. 341-349, August, 1987. Because this technique is restricted at high frequencies by the inadequate circuit model for the probe, a quasi-static analysis of a coaxial sensor has been proposed to formulate a more accurate equivalent model, Misra, A Quasi-Static Analysis of Open-ended Coaxial Lines, IEEE Trans. Microwave Theory Tech., Vol. MTT-35, pp. 925-928, October, 1987. In this method, a quasi-static approximation to the formula for the normalized aperture admittance (Y.sub.L) of an open-ended coaxial line terminated by a semi-infinite medium on a ground plane is given as: ##EQU1## where k=.omega..sqroot..mu..sub.0 .rho..sup.*, r=.vertline.p.sup.2 +p.sup.12 -2pp.sup.' cos.phi..vertline..sup.1/2, and a and b are the inner and outer radii of the coaxial aperture, k.sub.c =.omega..sqroot..mu..sub.0 .epsilon..sub.0 .epsilon..sub.c, .mu..sub.0 is the permeability of free space, .epsilon..sup.* is the complex permittivity of the semi-infinite medium, .epsilon..sub.c is the relative permittivity of the coaxial line and .omega. is the angular frequency of the electromagnetic fields. The calculations required to solve Equation 1 are time consuming and do not provide an easy method for determining the admittance of the sample.
Accordingly, a need persists for a method and apparatus for easily and accurately determining the complex permittivity of materials at microwave frequencies using an open-ended coaxial line. Such a method and apparatus should accurately relate, in real time, the measured parameters of a material such as the reflection coefficient or input impedance of the sample to dielectric properties of the sample at frequencies from about 100 MHz up to and above 20 GHz. Moreover, such a method and apparatus should be capable of measuring complex permittivity continuously or at frequent intervals.